Dispersion in a window pane. In the figure on the left, a beam of white light is incident at angle θ = 51° on a common window pane (shown in cross section). For the pane's type of glass, the index of refraction for visible light ranges from 1.528 at the blue end of the spectrum to 1.507 at the red end. The two sides of the pane are parallel. (Hint: When you look at an object through a window pane, are the colors in the light from the object dispersed as shown in the figure on the right, where chromatic dispersion occurs at the first surface and is increased at the second surface?)

What is the angular spread of the colors in the beam when the light enters the pane?

Use snell's law for each refracted angle.

sinTheta1=sin51 /1.507
sinTheta2=sin51 /1.528

calculate theta1, theta2, subtract one from the other.

To find the angular spread of the colors in the beam when the light enters the pane, we need to use the concept of angular dispersion.

Angular dispersion occurs when different colors of light are deviated or bent at different angles as they pass through a medium, such as a glass pane. The amount of angular dispersion depends on the refractive index of the medium for each color of light.

In this case, the window pane has different refractive indices for different colors of light. The refractive index is given as 1.528 for blue light and 1.507 for red light.

The angular spread of colors can be calculated using the formula:

Δθ = (n_blue - n_red) / n_blue

Where Δθ is the angular spread and n_blue and n_red are the refractive indices for blue and red light respectively.

Substituting the given values:

Δθ = (1.528 - 1.507) / 1.528

Δθ = 0.021 / 1.528

Δθ ≈ 0.014

Therefore, the angular spread of the colors in the beam when the light enters the pane is approximately 0.014 radians.

To calculate the angular spread of the colors in the beam when the light enters the pane, we can use the concept of angular dispersion.

Angular dispersion (Δθ) is given by the formula:

Δθ = (n_blue - n_red) * sin(θ)

where n_blue is the refractive index for blue light and n_red is the refractive index for red light.

Given:
n_blue = 1.528
n_red = 1.507
θ = 51°

Substituting these values into the formula, we get:

Δθ = (1.528 - 1.507) * sin(51°)

Calculating:

Δθ = 0.021 * sin(51°)

Using a calculator:

Δθ ≈ 0.021 * 0.777
Δθ ≈ 0.016

Therefore, the angular spread of the colors in the beam when the light enters the window pane is approximately 0.016 radians.